Linear optimization (or linear programming, LP) is the
fundamental branch of optimization, with applications to
many areas including life sciences, computer science,
defense, finance, telecommunications, transportation,
etc. Other types of optimization typically use LP as the
underlying model. This course will provide an integrated
view of the theory, solution techniques, and applications of
linear optimization. There will be a fair bit of emphasis on
theorems and their proofs. The treatment of most topics will
begin with a geometric point of view, followed by the
development of the solution techniques (algorithms), which
are described using linear algebra. A background in linear
algebra and multivariate calculus is assumed. Topics covered
include linear programming formulations, geometry of linear
programming, the simplex method, duality, sensitivity
analysis, interior point methods, and integer programming
basics. Apart from problems involving proofs, the student
will use Octave (or Matlab) or another programming language
(e.g., Python) for implementing some of the computations and
algorithms. A state-of-the-art modeling software such as
AMPL will
also be introduced for solving problems modeling real life
situations.